Given T = { even numbers from 1 to 12 }
N = {common factors of 6, 8 and 12}
Find T ∩ N
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(D)
{2}
2
What is the next number in the series 2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\)...
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(D)
\(\frac{1}{8}\)
3
If U = {x : x is an integer and 1 ≤ x ≤ 20 }
E1 = {x: x is a multiple of 3}
E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2
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(A)
\(\frac{3}{4}\)
4
The curved surface area of a cylinder 5cm high is 110cm2. Find the radius of its base
π = \(\frac{22}{7}\)
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(B)
3.5cm
5
If two graphs Y = px2 + q and y = 2x2 − 1 intersect at x =2, find the value of p in terms of q
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(B)
7 − \(\frac{q}{4}\)
6
Evaluate (\(\sin\)45º + \(\sin\)30º ) in surd form
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(D)
\(\frac{1 +\sqrt{2}}{2}\)
7
If y = x Sin x, find \(\frac{dy}{dx}\) when x = \(\frac{\pi}{2}\)
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(C)
1
8
If temperature t is directly proportional to heat h, and when t = 20oC, h = 50 J, find t when h = 60J
A man covered a distance of 50 miles on his first trip, on a later trip he traveled 300 miles while going 3 times as fast. His new time compared with the old distance was?
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(C)
twice as much
22
In the figure, find x
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(A)
40o
23
Divide 4x3 - 3x + 1 by 2x - 1
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(D)
2x2 + x -1
24
A car dealer bought a second-hand car for 250,000 and spent N 70,000 refurbishing it. He then sold the car for N400,000. What is the percentage gain?
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(C)
25%
25
Find the number of ways that the letters of the word EXCELLENCE be arranged
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(C)
\(\frac{10!}{4!2!2!}\)
26
Evaluate \(\frac{0.00000231}{0.007}\) and leave the answer in standard form
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(A)
3.3 x 10-4
27
If a rod 10cm in length was measured as 10.5cm, calculate the percentage error
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(A)
5%
28
Find the principal which amounts to ₦ 5,500 at a simple interest in 5 years at 2% per annum
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(B)
₦ 5,000
29
The pie chart shows the allocation of money to each sector in a farm. The total amount allocated to the farm is ₦ 80 000. Find the amount allocated to fertilizer
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(D)
₦ 20,000
30
In how many ways can the word MATHEMATICS be arranged?
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(C)
\(\frac{11!}{2!2!2!}\)
31
In how many ways can the word MACICITA be arranged?
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(C)
\(\frac{8!}{2! 2! 2!}\)
32
y is inversely proportional to x and y is 6 when x = 7. Find the constant of the variation
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(B)
42
33
Find the equation of the locus of a point p (x, y) such that pv = pw, where v= (1, 1) and w = (3, 5)
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(D)
x + 2y = 8
34
Find ∫(x2 + 3x − 5)dx
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(C)
\(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) - 5x + k
35
In the diagram above MN is a chord of a circle KMN centre O and radius 10cm. If < MON = 140°, find, to the nearest cm, the length of the chord MN.
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(B)
19cm
36
Factorize completely X2+2XY+Y2+3X+3Y-18
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(A)
(x + y + 6)(x + y -3)
37
Make S the subject of the relation
p = s + \(\frac{sm^2}{nr}\)
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(A)
s = \(\frac{nrp}{nr + m^2}\)
38
The operation * on the set R of real number is defined by x * y = 3x + 2y − 1, find 3* − 1
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(C)
6
39
Find the gradient of the line joining the points (3, 2) and (1, 4)
